A method for diagnosing and locating open-circuit faults of switching tubes of a power converter

Abstract

This invention relates to the field of power electronic converter fault diagnosis technology, specifically disclosing a method for diagnosing and locating open-circuit faults in power converter switching transistors. Taking single-phase-shift control as an example, to achieve open-circuit fault diagnosis in dual active full-bridge DC / DC converters, this invention first calculates the fundamental frequency and second harmonic amplitudes based on the sampled output voltage or current. When the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds a preset threshold, it is determined that an open-circuit fault has occurred in a switching transistor of the converter. To locate the open-circuit fault in the converter switching transistors, this invention analyzes and compares the harmonic characteristics of the output voltage or current under various open-circuit fault conditions, and designs a fault location algorithm accordingly. By calculating the expression of the fundamental frequency component of the output voltage or current, the open-circuit fault location of the dual active full-bridge DC / DC converter switching transistors is achieved. This invention does not require additional hardware circuits and components; it can accurately diagnose and locate open-circuit faults in switching transistors based solely on the electrical quantities on the converter output side. It is low-cost and highly accurate, providing a new diagnostic approach for fault diagnosis technology of dual active full-bridge DC / DC converters.

Description

Technical Field

[0001] This invention belongs to the field of power electronic converter fault diagnosis technology, specifically relating to a method for diagnosing and locating open-circuit faults in power converter switching transistors. Background Technology

[0002] Dual active full-bridge DC / DC converters, as isolated power electronic converters, offer advantages such as soft switching, high power density, and low electromagnetic interference, and have been widely used in numerous fields including electric vehicles, aerospace, and renewable energy. With increasing demands for the reliability of power electronic converters, fault diagnosis of dual active full-bridge DC / DC converters has received growing attention.

[0003] Due to the inherent characteristics of power electronic devices, switching elements are the most vulnerable components in a converter. During operation, switching elements are commonly damaged by environmental changes, transient shocks, overload operation, and thermal cycling. An open-circuit fault in the converter does not immediately cause system collapse, but it leads to a DC component in the internal current and an increase in current peak value, causing further failures in other components. Dual active bridge converters contain a large number of switching elements, and this number increases dramatically after modularization. Therefore, researching real-time diagnosis and location methods for open-circuit faults in the switching transistors of dual active full-bridge DC / DC converters is of great significance for improving maintenance efficiency and reducing system protection costs.

[0004] Currently, there are limited direct diagnostic methods applicable to dual active full-bridge DC / DC converters. Diagnostic algorithm design needs to achieve rapid fault detection and location using signals acquired and output by the control system, with minimal or no additional hardware. Most current diagnostic algorithms for dual active full-bridge DC / DC converters add a hardware detection circuit to obtain information such as converter arm voltage and inductor current, which is complex and costly. Furthermore, most current diagnostic algorithms cannot accurately locate open-circuit faults simultaneously. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for diagnosing and locating open-circuit faults in power converter switching transistors. This method does not require additional hardware circuits, and can accurately diagnose and locate open-circuit fault switching transistors based solely on the output voltage of the original electrical quantities in the converter control. The method is simple and has low hardware costs.

[0006] The present invention provides a method for diagnosing and locating open-circuit faults in power converter switching transistors. The technical solution is as follows: real-time acquisition of output-side voltage data of a dual active full-bridge DC / DC converter; innovative analysis of the harmonic content and characteristics of the output voltage; and combination with current control parameters to achieve diagnosis and location of open-circuit faults.

[0007] The present invention provides a method for diagnosing and locating open-circuit faults in power converter switching transistors, comprising the following steps:

[0008] Step 1: Calculate the fundamental frequency and second harmonic amplitude of the output voltage / current. When the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds the preset threshold, it is determined that there is an open circuit fault in the switching transistor of the dual active full-bridge DC / DC converter.

[0009] Step 2: Calculate the fundamental frequency coefficient of the Fourier series in exponential form based on the output voltage / current, extract its effective fault characteristic formula, and then compare and judge it with the comparison formula of each switch open circuit fault, so as to locate the switch of the dual active full bridge DC / DC converter with open circuit fault.

[0010] Step 1 specifically involves:

[0011] Step 1.1: Taking the output voltage of a dual active full-bridge DC / DC converter as an example, calculate the amplitudes of the fundamental frequency and second harmonic components of the output voltage under normal operation and fault conditions of each switch. The ratios of the amplitudes of the fundamental frequency and second harmonic components of the output voltage under normal operation, primary-side switch open-circuit fault, and secondary-side switch open-circuit fault conditions are respectively...

[0012] No faults:

[0013] Original side switch open circuit fault:

[0014] Secondary-side switch open circuit fault:

[0015] In the formula, The amplitude of the fundamental frequency component of the converter output voltage. Let d be the amplitude of the second harmonic component of the converter output voltage, d be the phase shift ratio under single-phase-shift control, T be the switching period, then dT be the phase shift time of the full bridge on the primary and secondary sides, N be the turns ratio of the high-frequency transformer, and U be the phase shift time of the secondary side. in U is the input voltage. o Let k be the output voltage, and define k = NU. in / U o ;

[0016] Step 1.2: Calculate the fundamental frequency (switching frequency) and second harmonic amplitude of the output voltage using the FFT algorithm. If the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds a preset threshold, a fault determination for an open circuit in the converter switching transistor is triggered. The fault determination condition is as follows:

[0017]

[0018] In the formula, X threshold This is a threshold that is preset based on the actual situation.

[0019] Step 2 specifically involves:

[0020] Step 2.1: Calculate the fundamental frequency coefficients of the exponential Fourier series for each switch under fault conditions, and extract its characteristic expression as a reference expression, specifically:

[0021] To calculate the fundamental frequency coefficients of the exponential Fourier series under each switch fault state, the following definition is made:

[0022]

[0023]

[0024] w1 = -1 + 4d + k

[0025] w2=1-k+4dk

[0026] In the formula, R and C are the capacitor and load resistance on the output side of the converter, respectively. The specific fundamental frequency coefficient under fault conditions for each switching transistor is:

[0027] S1 / S4 open circuit fault:

[0028] S2 / S3 open circuit fault:

[0029] Q1 / Q4 open circuit fault:

[0030] Q2 / Q3 open circuit fault:

[0031] Step 2.2: Calculate the fundamental frequency coefficient of the Fourier series of the output voltage. If step 1 determines that a switching transistor in the converter has an open-circuit fault, calculate the fault location criterion at this moment, specifically:

[0032] If step 1 determines that a switching transistor in the converter has an open-circuit fault, the acquired output voltage is processed using FFT to obtain the fundamental frequency coefficient of the Fourier series of the output voltage. Then, the fault location criterion w is defined as follows:

[0033]

[0034] Step 2.3: Compare the calculated fault location criteria with the characteristic formula of typical faults, and combine voltage gain and phase shift to determine the status of the switching transistor that has an open-circuit fault, thereby locating the open-circuit fault of the switching transistor in the dual active full-bridge DC / DC converter. Specifically:

[0035] Assume that \(0\leq d\leq0.25\) and \(k > 0\). According to the fault location criterion \(w\) calculated in step 2.2, combined with the quantitative relationship between \(k\) and \(d\) at this moment, the open - circuit switch tube is located according to the following criteria for judging the occurrence of an open - circuit fault

[0036] (1) When \(0 < k\leq1 - 4d\): If the criterion \(w\) is near \(w1\), it is determined that the switch tube \(Q1\) or \(Q4\) has an open - circuit fault; if the criterion \(w\) is near \(w2\), it is determined that the switch tube \(S1\) or \(S4\) has an open - circuit fault; if the criterion \(w\) is near \(-w1\), it is determined that the switch tube \(Q2\) or \(Q3\) has an open - circuit fault; if the criterion \(w\) is near \(-w2\), it is determined that the switch tube \(S2\) or \(S3\) has an open - circuit fault.

[0037] (2) When \(1 - 4d < k\leq1\): If the criterion \(w\) is near \(w1\), it is determined that the switch tube \(Q2\) or \(Q3\) has an open - circuit fault; if the criterion \(w\) is near \(w2\), it is determined that the switch tube \(S1\) or \(S4\) has an open - circuit fault; if the criterion \(w\) is near \(-w1\), it is determined that the switch tube \(Q1\) or \(Q4\) has an open - circuit fault; if the criterion \(w\) is near \(-w2\), it is determined that the switch tube \(S2\) or \(S3\) has an open - circuit fault.

[0038] (3) When \(k > 1\): If the criterion \(w\) is near \(w1\), it is determined that the switch tube \(S1\) or \(S4\) or \(Q2\) or \(Q3\) has an open - circuit fault; if the criterion \(w\) is near \(-w1\), it is determined that the switch tube \(S2\) or \(S3\) or \(Q1\) or \(Q4\) has an open - circuit fault.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. By detecting the output voltage / current of the converter, calculating its fundamental frequency and the amplitude of the second - harmonic, comparing and judging the ratio of the fundamental - frequency amplitude to the second - harmonic amplitude, the fast diagnosis of the open - circuit fault of the switch tube in the dual - active - bridge DC / DC converter is realized;

[0041] 2. If it is judged that the converter has an open - circuit fault of the switch tube, the expression of the fundamental - frequency component of the output voltage / current of the converter is further calculated and its fault - location criterion is extracted, combined with the characteristic formula calculated for typical faults, to realize the location of the open - circuit fault of the switch tube in the dual - active - bridge DC / DC converter;

[0042] 3. The present invention does not require additional hardware circuits, and only based on the output voltage of the electrical quantity originally in the converter control, the accurate diagnosis and location of the fault can be realized. The method is simple and the hardware cost is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is the circuit topology of the dual - active - bridge DC / DC converter

[0044] Figure 2 is the normal operation waveform of the dual - active - bridge DC / DC converter

[0045] Figure 3 Diagram showing an open-circuit fault in a dual active full-bridge DC / DC converter.

[0046] Figure 4 Waveform of a dual active full-bridge DC / DC converter operating under open-circuit fault conditions.

[0047] Figure 5 Flowchart for troubleshooting and locating open-circuit faults in dual active full-bridge DC / DC converter switches Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] To better understand this invention, the following introduction will be given before describing the invention.

[0050] like Figure 1 As shown, the dual active full-bridge DC / DC converter in this invention mainly consists of four parts: a primary-side full-bridge, an inductor L, a high-frequency transformer, and a secondary-side full-bridge. The primary-side full-bridge is composed of four switching transistors S1–S4 and their anti-parallel diodes D1–D4, while the secondary-side full-bridge is composed of four switching transistors Q1–Q4 and their anti-parallel diodes M1–M4.

[0051] Taking single-phase-shift control as an example, the normal operating waveform of a dual active full-bridge DC / DC converter is as follows: Figure 2 As shown in the diagram, the drive signal for each switch is a square wave signal with a 50% duty cycle under the same switching period T. The drive signals for the upper and lower switches in the same bridge arm are complementary, while the drive signals for the two diagonally opposite switches are the same. The phase shift time between the primary and secondary sides is dT. When the converter is operating normally, the ripple frequency of the voltage and current ripple on the converter output side is twice the switching frequency.

[0052] Next, we analyze the operating characteristics of the dual active full-bridge DC / DC converter under open-circuit fault conditions. For example... Figure 3 As shown, there are 8 types of open-circuit faults in the switching transistors, corresponding to the 8 switching transistors in the converter. Since the fault analysis in this invention takes single-phase-shift control as an example, the operating characteristics of open-circuit faults in diagonal switching transistors are the same. That is, open-circuit faults can be divided into 4 groups: S1 / S4 open-circuit fault; S2 / S3 open-circuit fault; Q1 / Q4 open-circuit fault; Q2 / Q3 open-circuit fault.

[0053] Figure 4The above are typical operating waveforms of a dual active full-bridge DC / DC converter under open-circuit fault conditions. Due to the fault of one switch, the operating characteristics of the converter change, which can be summarized as follows: When S1 / S4 is open-circuited, the inductor current generates a negative DC component and is constantly non-positive throughout the switching cycle; the pulsation frequency of the output current and voltage is equal to the switching frequency. When S2 / S3 is open-circuited, the inductor current generates a positive DC component and is constantly non-negative throughout the switching cycle; the pulsation frequency of the output current and voltage is equal to the switching frequency. When Q1 / Q4 is open-circuited, the inductor current generates a positive DC component, and the pulsation frequency of the output current and voltage is equal to the switching frequency. When S2 / S3 is open-circuited, the inductor current generates a negative DC component, and the pulsation frequency of the output current and voltage is equal to the switching frequency. In summary, while an open-circuit fault in a dual active full-bridge DC / DC converter does not affect power transmission, it does lead to the generation of a DC component in the inductor current, thereby altering the ripple frequency of the output voltage / current—that is, changing the frequency composition of the output electrical quantities. Therefore, this invention diagnoses and locates open-circuit faults in the dual active full-bridge DC / DC converter by performing frequency analysis on the output voltage / current.

[0054] Next, we will analyze the output frequency components of the dual active full-bridge DC / DC converter under normal operation and open-circuit fault conditions.

[0055] For a periodic signal f(x), it can be represented by an exponential Fourier series expansion, which is:

[0056]

[0057] in The amplitude of the nth harmonic component of the signal is 2|C n Therefore, C n Amplitude | C n The amplitude of the signal is proportional to the amplitude of its nth harmonic component, therefore it will be transmitted through C. n Calculate and analyze frequency components.

[0058] Define the switching functions of the primary and secondary sides of the full bridge as g, respectively. P (t) and g S (t), then g P (t) and g S (t) can be expressed as follows:

[0059]

[0060]

[0061] The fundamental frequency component of the output voltage is defined as follows:

[0062]

[0063] χ=jZ1e -j2πd

[0064]

[0065] w1 = -1 + 4d + k

[0066] w2=1-k+4dk

[0067] When 2πnf s When RC >> 1, it can be considered that It can be derived that the fundamental frequency Fourier series coefficients of the output voltage of the dual active full-bridge DC / DC converter under normal operation and open-circuit fault conditions are:

[0068]

[0069] The coefficients of the second harmonic Fourier series of the output voltage are the same regardless of which switching transistor is faulty; specifically:

[0070]

[0071] The present invention provides a method for diagnosing and locating open-circuit faults in power converter switching transistors. The technical solution is as follows: real-time acquisition of output-side voltage data of a dual active full-bridge DC / DC converter; innovative analysis of the harmonic content and characteristics of the output voltage; and combination with current control parameters to achieve diagnosis and location of open-circuit faults.

[0072] This invention provides a method for diagnosing and locating open-circuit faults in power converter switching transistors, such as... Figure 5 As shown, it includes the following steps:

[0073] Step 1: Calculate the fundamental frequency and second harmonic amplitude of the output voltage / current. When the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds the preset threshold, it is determined that there is an open circuit fault in the switching transistor of the dual active full-bridge DC / DC converter.

[0074] Step 2: Calculate the fundamental frequency coefficient of the Fourier series in exponential form based on the output voltage / current, extract its effective fault characteristic formula, and then compare and judge it with the comparison formula of each switch open circuit fault, so as to locate the switch of the dual active full bridge DC / DC converter with open circuit fault.

[0075] Step 1 specifically involves:

[0076] Step 1.1: Taking the output voltage of a dual active full-bridge DC / DC converter as an example, calculate the amplitudes of the fundamental frequency and second harmonic components of the output voltage under normal operation and fault conditions of each switch. The ratios of the amplitudes of the fundamental frequency and second harmonic components of the output voltage under normal operation, primary-side switch open-circuit fault, and secondary-side switch open-circuit fault conditions are respectively...

[0077] No faults:

[0078] Original side switch open circuit fault:

[0079] Secondary-side switch open circuit fault:

[0080] In the formula, The amplitude of the fundamental frequency component of the converter output voltage. Let d be the amplitude of the second harmonic component of the converter output voltage, d be the phase shift ratio under SPS control, T be the switching period, then dT be the phase shift time of the full bridge on the primary and secondary sides, N be the turns ratio of the high-frequency transformer, and U be the phase shift time of the secondary side. in U is the input voltage. o Let k be the output voltage, and define k = NU. in / U o ;

[0081] Step 1.2: Calculate the fundamental frequency (switching frequency) and second harmonic amplitude of the output voltage using the FFT algorithm. If the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds a preset threshold, a fault determination for an open circuit in the converter switching transistor is triggered. The fault determination condition is as follows:

[0082]

[0083] In the formula, X threshold This is a threshold that is preset based on the actual situation.

[0084] Step 2 specifically involves:

[0085] Step 2.1: Calculate the fundamental frequency coefficients of the exponential Fourier series for each switch under fault conditions, and extract its characteristic expression as a reference expression, specifically:

[0086] To calculate the fundamental frequency coefficients of the exponential Fourier series under each switch fault state, the following definition is made:

[0087]

[0088]

[0089] w1=+1+4d+k

[0090] w2=1+k+4dk

[0091] In the formula, R and C are the capacitor and load resistor on the output side of the converter, respectively. The fundamental frequency coefficients under the faults of each switching tube are specifically as follows

[0092] Open-circuit fault of S1 / S4:

[0093] Open-circuit fault of S2 / S3:

[0094] Open-circuit fault of Q1 / Q4:

[0095] Open-circuit fault of Q2 / Q3:

[0096] Step 2.2: Calculate the fundamental frequency coefficient of the output voltage Fourier series. If it is determined in Step 1 that there is an open-circuit fault in the switching tube of the converter, calculate the fault position criterion at this moment, specifically as follows:

[0097] If it is determined in Step 1 that there is an open-circuit fault in the switching tube of the converter, the collected output voltage is calculated and processed through FFT to obtain the fundamental frequency coefficient of the output voltage Fourier series. Then, define the fault position criterion w as

[0098]

[0099] Step 2.3: Compare the calculated fault position criterion with the characteristic formula of the typical fault, and combine the voltage gain and phase shift to judge the situation of the open-circuit fault of the switching tube, so as to locate the open-circuit fault of the switching tube of the dual-active-bridge DC / DC converter, specifically as follows:

[0100] Assume 0≤d≤0.25 and k>0. According to the fault position criterion w calculated in Step 2.2, and combined with the quantitative relationship between k and d at this moment, the switching tube where the open-circuit fault occurs is located according to the following criteria

[0101] (1) When 0<k≤1 - 4d: If the criterion w is near w1, it is determined that the switching tube Q1 or Q4 has an open-circuit fault; if the criterion w is near w2, it is determined that the switching tube S1 or S4 has an open-circuit fault; if the criterion w is near -w1, it is determined that the switching tube Q2 or Q3 has an open-circuit fault; if the criterion w is near -w2, it is determined that the switching tube S2 or S3 has an open-circuit fault.

[0102] (2) When 1 - 4d<k≤1: If the criterion w is near w1, it is determined that the switching tube Q2 or Q3 has an open-circuit fault; if the criterion w is near w2, it is determined that the switching tube S1 or S4 has an open-circuit fault; if the criterion w is near -w1, it is determined that the switching tube Q1 or Q4 has an open-circuit fault; if the criterion w is near -w2, it is determined that the switching tube S2 or S3 has an open-circuit fault.

[0103] (3) When k>1: If the criterion w is near w1, then the switch S1 or S4 or Q2 or Q3 is determined to have an open circuit fault; if the criterion w is near -w1, then the switch S2 or S3 or Q1 or Q4 is determined to have an open circuit fault.

[0104] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0105] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for diagnosing and locating open-circuit faults in the switching transistors of a dual active full-bridge DC / DC converter, characterized in that: Step 1: Calculate the fundamental frequency and second harmonic amplitude of the output voltage or current. When the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds the preset threshold, it is determined that there is an open circuit fault in the switching transistor of the dual active full-bridge DC / DC converter. Step 2: Calculate the fundamental frequency coefficient of the Fourier series in exponential form based on the output voltage or current, extract its effective fault characteristic formula, and then compare and judge it with the comparison formula of each switch open circuit fault, so as to locate the switch of the dual active full bridge DC / DC converter with open circuit fault. Step 1 specifically involves: Step 1.1: Taking the output voltage of a dual active full-bridge DC / DC converter as an example, calculate the fundamental frequency and second harmonic amplitude of the output voltage under normal operation and fault conditions of each switch. The ratios of the fundamental frequency and second harmonic amplitude of the output voltage under normal operation, primary-side switch open-circuit fault, and secondary-side switch open-circuit fault conditions are respectively... No faults: Original side switch open circuit fault: Secondary-side switch open circuit fault: In the formula, The amplitude of the fundamental frequency component of the converter output voltage. The amplitude of the second harmonic of the converter output voltage. d For the phase shift under single-phase control, T For the switching cycle, then dT This refers to the phase shift time of the entire bridge on the original secondary side. N For the turns ratio of a high-frequency transformer, U in Input voltage, U o The output voltage is defined as follows: k = NU in / U o ; Step 1.2: Calculate the fundamental frequency and second harmonic amplitude of the output voltage using the FFT algorithm. If the ratio of the fundamental frequency amplitude to the second harmonic amplitude exceeds a preset threshold, a fault determination for an open circuit in the converter switching transistor is triggered. The fault determination condition is as follows: In the formula, A threshold set in advance based on actual conditions; Step 2 specifically involves: Step 2.1: Calculate the fundamental frequency coefficients of the exponential Fourier series under each switch fault state, and extract its characteristic expression as a reference expression; Step 2.2: Calculate the fundamental frequency coefficient of the Fourier series of the output voltage. If Step 1 determines that there is an open circuit fault in the converter's switching transistor, calculate the fault location criterion at this moment. Step 2.3: Compare the calculated fault location criteria with the characteristic formula of typical faults, and combine the voltage gain and phase shift to determine the status of the switch that has an open circuit fault, thereby locating the open circuit fault of the switch in the dual active full-bridge DC / DC converter.

2. The method for diagnosing and locating open-circuit faults in dual active full-bridge DC / DC converters according to claim 1, characterized in that, Step 2.1 specifically involves: To calculate the fundamental frequency coefficients of the exponential Fourier series under each switch fault state, the following definition is made: In the formula, R and C These are the capacitor and load resistor on the output side of the converter, respectively. f s For the converter switching frequency, , , and As an intermediate variable, the fundamental frequency coefficient under each switching transistor fault is specifically as follows: S1 / S4 open circuit fault: S2 / S3 open circuit fault: Q1 / Q4 open circuit fault: Q2 / Q3 open circuit fault: .

3. The method for diagnosing and locating open-circuit faults in dual active full-bridge DC / DC converters according to claim 1, characterized in that, Step 2.2 specifically involves: If step 1 determines that a switching transistor in the converter has an open-circuit fault, the acquired output voltage is processed using FFT to obtain the fundamental frequency coefficient of the Fourier series of the output voltage. Then, the fault location criterion is defined. w for 。 4. The method for diagnosing and locating open-circuit faults in dual active full-bridge DC / DC converters according to claim 1, characterized in that, Step 2.3 specifically involves: Assume 0≤ d ≤0.25 and k >0, based on the fault location criterion calculated in step 2.2 w And combined with the present moment k and d The quantitative relationship between them is determined according to the following criteria to pinpoint the location of the open-circuit fault in the switch transistor. (1) When 0 < k ≤1−4 d Time: If the criterion w exist w If the fault is near 1, then it is determined that either switch Q1 or Q4 has an open circuit fault; if the criterion is... w exist w If the fault is near 2, then it is determined that switch S1 or S4 has an open circuit fault; if the criterion is... w In − w If the fault is near 1, then it is determined that either switch Q2 or Q3 has an open circuit fault; if the criterion is... w In − w If the circuit is near 2, it is determined that either switch S2 or S3 has an open circuit fault; (2) When 1−4 d < k When ≤1: if the criterion w exist w If the fault is near 1, then it is determined that either switch Q2 or Q3 has an open circuit fault; if the criterion is... w exist w If the fault is near 2, then it is determined that switch S1 or S4 has an open circuit fault; if the criterion is... w In − w If the fault is near 1, then it is determined that either switch Q1 or Q4 has an open circuit fault; if the criterion is... w In − w If the circuit is near 2, it is determined that either switch S2 or S3 has an open circuit fault; (3) When k >1: If the criterion w exist w If the fault is near 1, then it is determined that switch S1, S4, Q2, or Q3 has an open circuit fault; if the criterion is... w In − w If the value is near 1, then it is determined that the switching transistor S2, S3, Q1, or Q4 has an open circuit fault.

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